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Another unfortunate experiment – the Numeracy Project

Another experiment is being conducted without informed consent on New Zealand’s citizens – but it is not on our women, this time.  It is on our children.  The experiment is called the Numeracy Project, and its victims are beginning to become visible in the ranks of those who are now beginning to enter our secondary schools.

Ask parents and teachers about the teaching of mathematics in the Numeracy Project and there will be polarized views…but bit by bit, as the much-vaunted gains it will bring to the mathematical ability of the nation’s primary school children prove elusive, a ground swell of concern is growing.  Refugees from the Numeracy Project are to be found in just about every new entrant to our school in Year 4 and above; they sigh in relief when they hear that we do not teach the Numeracy Project.

The Numeracy Project began in 2000.  It was touted as a revolutionary improvement to the way mathematics was taught in New Zealand schools…and it certainly was a change.  Millions of dollars has been poured into curriculum development consultants, into professional development for teachers, into the purchase of new school resources, and into research into the effects of the Numeracy Project.  It is one big action research project – the children in most schools are being experimented on and none of them, nor their parents, have any option to being part of it.  Soon there will be only a handful of teachers left in just a few schools who know any other way of teaching mathematics than the Numeracy Project way.

Here’s a quote from the Ministry of Education mathematics website: “The biggest difference in schools involved in the Numeracy Project is that children are encouraged to learn a range of different ways to solve problems and to choose the most appropriate one for each problem. You may be familiar with certain ‘rules’ for doing maths. While these will still work, your child may learn different ways to solve problems. Often these methods involve mental strategies, or working things out in your head, rather than written methods.

By “rules” one can only guess that the writer means algorithms (sums) or mathematical conventions like “order of operations”.  The strange thing is, there are no “rules” for solving problems – either you choose a solution that works, or you do not.  The solution will probably involve calculations and it is in choosing the correct operations (addition, subtraction, multiplication or division) and applying them in the correct order to the appropriate numbers that one arrives at the correct solution.  What you are hearing in this quote is some sort of put down of “traditional” mathematics in the form of sums and the elevation of mental computation.  We can have no beef with the latter – bring on greater mental acuity in mathematics – but in the put-down of “rules” we should hear warning bells about where this whole project is leading.  Mathematics, after all, is a subject with many rules which make it an international language to explain the real world. Learning these rules is actually what makes mathematics understandable, and being able to write them in a way that other people can understand is a vital part of real mathematics.

Another quote from the Ministry of Education: “This change in approach to maths education reflects changes in the world that impact on the maths that people need to know. Employers are increasingly looking for staff that have problem solving skills and an understanding of concepts, rather than just the ability to follow rules for calculatingThe increasing use of technology has also meant that a calculator or computer is almost always available in the workplace for larger calculations.”

How very enticing – an invitation to a world where you don’t really need much mathematical knowledge, just pull out the calculator!  Since when have employers ever not wanted people who have problem-solving skills or an understanding of concepts?  This is hollow justification. Ever wondered what the socialisation of education looks like? This is a classic example. Where in the above quote do you get a sense that the writer is thinking of children who might aspire to become engineers, doctors, pilots, architects or technicians? Where in this quote do you get a sense of the education system seeking to seed pure mathematics that leads to a secondary education in mathematics let alone a tertiary education? This is education for the working masses who apparently do not really need much mathematics!

And that is what the Numeracy Project seems to be delivering – children who have a range of informal number strategies, who can apply them to some degree and who might sometimes get the correct answer, although that is not as important as having a range of strategies.  Each year we test Year 7 new entrant pupils to our school, many of whom are intellectually very able, on their mathematical ability using a short Year 6 level test. Every year, the result is truly scary – most pupils cannot complete most of the tasks and the success rate on the problems is less than 30%.  Something is wrong.

The National Educational Monitoring Project is a cyclical monitoring of the educational achievements of New Zealand primary schools in each of the taught subjects.  In 2009,NEMP released its latest review of achievement in Mathematics.  In the summary, the report says, “On average, there was no meaningful change in number task performance between 2005 and 2009, for either year 4 or year 8 students. There was clear evidence of substantial change in the number task strategies that students use. These appeared to help with some tasks and hinder with others.

After almost ten years of a radical new teaching programme in Mathematics, one that is intended to revolutionise achievement levels in this subject, you would expect to see at least some useful upturn in pupil achievement levels after ten years, surely.  After all, many of the children being monitored will have had nothing but the Numeracy Project style of teaching in their mathematics.  The result – no improvements, nothing.  In fact, worse!  The NEMP report says that the Numeracy Project (number task strategies) “appeared to help with some tasks and hinder with others”.  What sort of radical new teaching programe is worth following when it “hinders” the very learning it is designed to improve? Something is very wrong here – no improvements and hindered learning.

There have been many research projects endeavouring to trace the improvement of mathematical thinking by pupils using the Numeracy Project approach.  Unfortunately, even after all this time, no significant development has been found in mathematical achievement.  Of course, by now, it is hard to find significant groups of pupils who have not been exposed to the Numeracy Project, so comparisons with a control group are impossible.  Worryingly, even at NCEA Level 1 when we might expect some effect, we do not see Numeracy Project pupils gaining significantly different results.

The background research on which the Numeracy Project is based has shown that number concept development in children progresses through several stages of increasing complexity.  The Numeracy Project takes this research and creates a series of teaching stages in which mastery of each stage is a prerequisite to entry to the next; a linear step-wise progression which looks great on paper but which, as in all endeavours to capture the complexity of human learning, fails to allow for the variation in progress of pupils’ mathematical learning.

Certainly, there are significant changes in the form of number concept in the early stages of mathematical development.  But, in the same way that learning a foreign language feeds on itself the more you use it, so number concepts develop from the simple and morph into complex interactions of number ideas which feed off each other, developing in myriad ways that defy the desire of academics to marshall them into neat linear step-wise learning pathways that all children follow.  Learning in mathematics is a continual interplay of concepts which link and relate backwards allowing leaps of understanding that take the learner in a journey characterised by times of rapid non-linear connection of concepts from different parts of the mathematical realm and slower times of consolidation and reinforcement. But that does not stop curriculum gurus developing a one-size-fits-all linear pathway for learning – and foisting it on the poor teacher.

So we have the sad situation where the Numeracy Project demands that the teacher teaches only number strategies that are within the next stage of the number development of a pupil, and forbids the teaching of algorithms (sums) at all until Stage 7 – somewhere around Year 6, 7 or 8.  No algorithms until Year 6, 7 or 8!  The theory is that until a child has reached an appropriate understanding of number, doing algorithms will somehow impede their learning.  There is no research evidence for this at all - it is pure ideology at work.  A mantra of “out with old, in with the new” has taken hold.  Teachers, and pupils, are coming to believe that horizontal methods of calculation are superior to the traditional vertical, and anything more complex than a two-digit operation is handed over to the ubiquitous calculator.  We are handing our children’s brains over to the tyranny of the battery.

Not teaching the use of algorithms until Year 6, 7 or 8 flies in the face of common sense, the practice of almost every other nation on earth and the evidence of hundreds of years of teaching.  Algorithms are the most sophisticated of number strategies.  Every algorithm not only is itself a sophisticated number strategy for obtaining the correct answer to complex operations, but it provides a perfect and appropriate context for applying, reinforcing and developing the simple number strategies that pupils are in the process of assimilating in primary school.

Our number system is based on the vertical column – that is its strength.  More than that, the relationship between the numbers in their columns lays down the basis upon which powerful mathematical understandings are based.  That is not to say that horizontal operations of a mental nature should not be fostered – of course they should, as these will aid rapid mental computation. Where the Numeracy project gurus have gone wrong is in their debasing vertical computation and delaying the teaching of algorithms.

To leave the learning of the process of algorithms to the last couple of years of primary school, when overall time spent on mathematics is reduced and geometry, statistics and algebra take a much more significant proportion of that teaching time, is to ensure that most pupils will not have internalised the algorithm processes in all their variations by the time they reach secondary school, and will have missed significant reinforcement of the way numbers work together.

But it gets worse.  One of the Numeracy Project requirements is that pupils must be able to show more than one strategy for solving a mathematical task – ability to show a number of strategies to solve the same problem indicates a higher level of complexity of mathematical knowledge.  That is fine for able pupils. But for those pupils to whom mathematical understandings do not come easily, just finding one strategy that works is an achievement – and it is a real achievement.  After all, we use mathematics to get answers to problems; when you get the answer, you have achieved the purpose.  But when, having found one working strategy, a pupil is asked to find other strategies, and fails to do so, and this happens again and again in their mathematics at school, he/she begins to feel a failure; even though he/she may have found one valid strategy.  It is pretty damning that an “innovative” new teaching programme should have as one of its outcomes pupils who believe that they are “dumb” at mathematics because they cannot find multiple strategies for a problem. That is one of the unfortunate outcomes of the Numeracy Project.

Unfortunately, not many schools have stood aside from the Numeracy Project, not even many independent schools which might have been expected to take a challenging view of such untested teaching methods. It could well be that The Cathedral Grammar School is the only Christchurch school not to have adopted this approach although there are many teachers throughout the city who quietly ignore the Numeracy Project requirements.

In this we see a really important reason for the existence of independent schools – what other educational group can have the disinterest to recognise failure in a Ministry of Education initiative for what it is and to announce that the educational king has no clothes?  The Numeracy Project is failing our nation’s primary school children in a critical subject at a critical age – and we should be very worried because the Numeracy Project is now entering our secondary schools.


National Standards – another good reason for Independent Schools!

It has been quiet on the National Standards front for a while – you could be excused for thinking that after initial resistance, National Standards were now an accepted part on the educational landscape.  They are not.

The Primary Principal\’s Federation recently passed a vote of no-confidence  “in the education policy and direction of the current government, in relation to National Standards, as led by the Minister”.  I suspect that we will see further such votes of no confidence by the teachers’ unions and by the School Trustees Association.  Things are hotting up in the state education world vis-à-vis National Standards.  Expect increasing opposition during this year.

Measuring a stick and calling it "short" does not make it longer!

The depth of public understanding about the detail of the current National Standards is abysmal.  Witness a letter to The Press on Monday, 11th April which talked about “accurate measurements (standards) to assess specific progress” as if National Standards did indeed provide these.  If you want to read more about the National Standards, there is a whole section of GrammarNet devoted to it.

At a broad conceptual level, a notion of National Standards, standards which are nation-wide, measurable and educationally valid, appears to have everything going for it.  The trouble is, as discovered by the United Kingdom and every other country that has tried the concept, it is not possible to write standards which are accepted nationwide, which are measurable in any way which would be acceptably accurate and which have educational merit – that is, they assist with educational achievement. That is a strike out on every point.  It is a pity the New Zealand has to find this out the hard way; we could just look at the sad experiences of other countries.

It is sad, because National Standards were principally introduced to help advance the performance of those pupils in the bottom 20% of achievement .  If anything, National Standards will hurt this group the most, through negative labelling twice a year and through the waste of millions of dollars that could have been spent on direct assistance to these pupils.

It is sad because state and integrated schools have no option but to implement these National Standards, deeply flawed as they are, and no matter how much their principal, staff and parents disagree with them.  If you wanted a really good reason for the existence of independent schools, here it is!  We can stand aside from this mess, watch the carnage from the sidelines and make comment while not fearing for our professional careers, or for the result of yet another experiment on our children/pupils.

It is sad because of the wasted effort involved.  Even if conceptually, the National Standards could be standardised and moderated, what would be the outcome?  Those parents with children who were “above” or “at” the standard would not be surprised – these people generally know where they are in the scale of relative ability.  Those parents with children performing “below” the standard have probably always known this to be the case (and certainly would have known if the school had been doing its job properly), in which case all we have done is raise the levels of anxiety and concern. So what has been achieved?

Schools and teachers do not need National Standards to identify under-achievers and those with learning issues – we have any number of tools to tell us how far behind the rest of the population such pupils lag.  Moving their achievement forward has much more to do with individualised intervention, social and family issues and resourcing of schools.  Putting money into targeted intervention would do much more than what National Standards could ever hope to achieve.

The Cathedral Grammar School does not report against National Standards – to do so would be to accept that the standards have some internal and external validity which they do not have.  What we have done is provide our parents with descriptions of what can be expected of a nationally average pupil at different year levels.  Parents can then assess their child against these to confirm for themselves if their child is at, above or below average expectations.  That nationally average pupil is one defined by testing of thousands of pupils over many years on valid test instruments. More importantly, as a pupil progresses through the school, his/her result on standardised tests are monitored – these are the real “accurate measurements…to assess specific progress”, not some subjective judgements by teachers working with a local perspective.

The teachers at our school, in the meantime, will be focused on the real task of moving each pupil, no matter their current  ability level, forward to the next level, just as quickly as that pupil can absorb the learning and skills required.  It will be child-focused, it will avoid labelling and it will be the greatest rate of development that each child can make.  That is what National Standards was meant to achieve…but never will.

Measuring a stick and calling it “short” does not make it grow longer!

Principal's welcome

Welcome to The Cathedral Grammar School, and to ‘the ideal preparation’ for your child for the future!

With a 130-year plus history, Cathedral Grammar is the longest established, private primary school in New Zealand. We take huge pride in the varied, successful and happy lives of the boys and girls who have experienced ‘Grammar’ over that time.

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